In the ICSE Class 9 Mathematics curriculum, the topic of theorems on area typically covers various theorems and concepts related to the calculation of area in different geometric shapes. Here’s a summary of the key theorems and concepts:

1. **Area of a Triangle**: The area of a triangle can be calculated using the formula A = 1/2 * base * height, where the base is the length of the triangle’s base and the height is the perpendicular distance from the base to the opposite vertex.

2. **Area of a Parallelogram**: The area of a parallelogram is equal to the product of its base and height, i.e., A = base * height.

3. **Area of a Trapezium**: The area of a trapezium is equal to half the sum of the lengths of its parallel sides multiplied by the height, i.e., A = 1/2 * (a + b) * h, where ‘a’ and ‘b’ are the lengths of the parallel sides and ‘h’ is the height.

4. **Area of a Rhombus**: The area of a rhombus can be calculated as half the product of its diagonals, i.e., A = 1/2 * d1 * d2, where ‘d1’ and ‘d2’ are the lengths of the diagonals.

5. **Area of a Circle**: The area of a circle is given by the formula A = π * r^2, where ‘r’ is the radius of the circle and π (pi) is a constant approximately equal to 3.14159.

6. **Pythagoras Theorem**: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where ‘a’ and ‘b’ are the lengths of the two shorter sides (legs) and ‘c’ is the length of the hypotenuse.

These theorems and formulas are essential for calculating the areas of different geometric shapes and are foundational concepts in geometry and mathematics.